Fuzzy Logic

Fuzzy Logic is becoming an essential method of solving problems in all domains. It gives tremendous impact on the design of autonomous intelligent systems. The purpose of this book is to introduce Hybrid Algorithms, Techniques, and Implementations of Fuzzy Logic. The book consists of thirteen chapters highlighting models and principles of fuzzy logic and issues on its techniques and implementations. The intended readers of this book are engineers, researchers, and graduate students interested in fuzzy logic systems

Online Learning for Ground Trajectory Prediction

This paper presents a model based on an hybrid system to numerically simulate the climbing phase of an aircraft. This model is then used within a trajectory prediction tool. Finally, the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) optimization algorithm is used to tune five selected parameters, and thus improve the accuracy of the model. Incorporated within a trajectory prediction tool, this model can be used to derive the order of magnitude of the prediction error over time, and thus the domain of validity of the trajectory prediction. A first validation experiment of the proposed model is based on the errors along time for a one-time trajectory prediction at the take off of the flight with respect to the default values of the theoretical BADA model. This experiment, assuming complete information, also shows the limit of the model. A second experiment part presents an on-line trajectory prediction, in which the prediction is continuously updated based on the current aircraft position. This approach raises several issues, for which improvements of the basic model are proposed, and the resulting trajectory prediction tool shows statistically significantly more accurate results than those of the default model.Comment: SESAR 2nd Innovation Days (2012

Power Quality Disturbance Detection and Classification

Power quality (PQ) monitoring is an essential service that many utilities perform for their industrial and larger commercial customers. Detecting and classifying the different electrical disturbances which can cause PQ problems is a difficult task that requires a high level of engineering knowledge. The vast majority of the disturbances are non-stationary and transitory in nature subsequently it requires advanced instruments and procedures for the examination of PQ disturbances. In this work a hybrid procedure is utilized for describing PQ disturbances utilizing wavelet transform and fuzzy logic. A no of PQ occasions are produced and decomposed utilizing wavelet decomposition algorithm of wavelet transform for exact recognition of disturbances. It is likewise watched that when the PQ disturbances are contaminated with noise the identification gets to be troublesome and the feature vectors to be separated will contain a high amount of noise which may corrupt the characterization precision. Consequently a Wavelet based denoising system is proposed in this work before feature extraction process. Two extremely distinct features basic to all PQ disturbances like Energy and Total Harmonic Distortion (THD) are separated utilizing discrete wavelet transform and is nourished as inputs to the fuzzy expert system for precise recognition and order of different PQ disturbances. The fuzzy expert system classifies the PQ disturbances as well as demonstrates whether the disturbance is unadulterated or contains harmonics. A neural network based Power Quality Disturbance (PQD) recognition framework is additionally displayed executing Multilayer Feedforward Neural Network (MFNN)

Learning Nonlinear Loop Invariants with Gated Continuous Logic Networks (Extended Version)

Verifying real-world programs often requires inferring loop invariants with nonlinear constraints. This is especially true in programs that perform many numerical operations, such as control systems for avionics or industrial plants. Recently, data-driven methods for loop invariant inference have shown promise, especially on linear invariants. However, applying data-driven inference to nonlinear loop invariants is challenging due to the large numbers of and magnitudes of high-order terms, the potential for overfitting on a small number of samples, and the large space of possible inequality bounds. In this paper, we introduce a new neural architecture for general SMT learning, the Gated Continuous Logic Network (G-CLN), and apply it to nonlinear loop invariant learning. G-CLNs extend the Continuous Logic Network (CLN) architecture with gating units and dropout, which allow the model to robustly learn general invariants over large numbers of terms. To address overfitting that arises from finite program sampling, we introduce fractional sampling---a sound relaxation of loop semantics to continuous functions that facilitates unbounded sampling on real domain. We additionally design a new CLN activation function, the Piecewise Biased Quadratic Unit (PBQU), for naturally learning tight inequality bounds. We incorporate these methods into a nonlinear loop invariant inference system that can learn general nonlinear loop invariants. We evaluate our system on a benchmark of nonlinear loop invariants and show it solves 26 out of 27 problems, 3 more than prior work, with an average runtime of 53.3 seconds. We further demonstrate the generic learning ability of G-CLNs by solving all 124 problems in the linear Code2Inv benchmark. We also perform a quantitative stability evaluation and show G-CLNs have a convergence rate of $97.5\%$ on quadratic problems, a $39.2\%$ improvement over CLN models

On-the-fly synthesizer programming with rule learning

This manuscript explores automatic programming of sound synthesis algorithms within the context of the performative artistic practice known as live coding. Writing source code in an improvised way to create music or visuals became an instrument the moment affordable computers were able to perform real-time sound synthesis with languages that keep their interpreter running. Ever since, live coding has dealt with real time programming of synthesis algorithms. For that purpose, one possibility is an algorithm that automatically creates variations out of a few presets selected by the user. However, the need for real-time feedback and the small size of the data sets (which can even be collected mid-performance) are constraints that make existing automatic sound synthesizer programmers and learning algorithms unfeasible. Also, the design of such algorithms is not oriented to create variations of a sound but rather to find the synthesizer parameters that match a given one. Other approaches create representations of the space of possible sounds, allowing the user to explore it by means of interactive evolution. Even though these systems are exploratory-oriented, they require longer run-times. This thesis investigates inductive rule learning for on-the-fly synthesizer programming. This approach is conceptually different from those found in both synthesizer programming and live coding literature. Rule models offer interpretability and allow working with the parameter values of the synthesis algorithms (even with symbolic data), making preprocessing unnecessary. RuLer, the proposed learning algorithm, receives a dataset containing user labeled combinations of parameter values of a synthesis algorithm. Among those combinations sharing the same label, it analyses the patterns based on dissimilarity. These patterns are described as an IF-THEN rule model. The algorithm parameters provide control to define what is considered a pattern. As patterns are the base for inducting new parameter settings, the algorithm parameters control the degree of consistency of the inducted settings respect to the original input data. An algorithm (named FuzzyRuLer) able to extend IF-THEN rules to hyperrectangles, which in turn are used as the cores of membership functions, is presented. The resulting fuzzy rule model creates a map of the entire input feature space. For such a pursuit, the algorithm generalizes the logical rules solving the contradictions by following a maximum volume heuristics. Across the manuscript it is discussed how, when machine learning algorithms are used as creative tools, glitches, errors or inaccuracies produced by the resulting models are sometimes desirable as they might offer novel, unpredictable results. The evaluation of the algorithms follows two paths. The first focuses on user tests. The second responds to the fact that this work was carried out within the computer science department and is intended to provide a broader, nonspecific domain evaluation of the algorithms performance using extrinsic benchmarks (i.e not belonging to a synthesizer's domain) for cross validation and minority oversampling. In oversampling tasks, using imbalanced datasets, the algorithm yields state-of-the-art results. Moreover, the synthetic points produced are significantly different from those created by the other algorithms and perform (controlled) exploration of more distant regions. Finally, accompanying the research, various performances, concerts and an album were produced with the algorithms and examples of this thesis. The reviews received and collections where the album has been featured show a positive reception within the community. Together, these evaluations suggest that rule learning is both an effective method and a promising path for further research.Aquest manuscrit explora la programació automàtica d’algorismes de síntesi de so dins del context de la pràctica artística performativa coneguda com a live coding. L'escriptura improvisada de codi font per crear música o visuals es va convertir en un instrument en el moment en què els ordinadors van poder realitzar síntesis de so en temps real amb llenguatges que mantenien el seu intèrpret en funcionament. D'aleshores ençà, el live coding comporta la programació en temps real d’algorismes de síntesi de so. Per a aquest propòsit, una possibilitat és tenir un algorisme que creï automàticament variacions a partir d'alguns presets seleccionats. No obstant, la necessitat de retroalimentació en temps real i la petita mida dels conjunts de dades són restriccions que fan que els programadors automàtics de sintetitzadors de so i els algorismes d’aprenentatge no siguin factibles d’utilitzar. A més, el seu disseny no està orientat a crear variacions d'un so, sinó a trobar els paràmetres del sintetitzador que aplicats a l'algorisme de síntesi produeixen un so determinat (target). Altres enfocaments creen representacions de l'espai de sons possibles, per permetre a l'usuari explorar-lo mitjançant l'evolució interactiva, però requereixen temps més llargs. Aquesta tesi investiga l'aprenentatge inductiu de regles per a la programació on-the-fly de sintetitzadors. Aquest enfocament és conceptualment diferent dels que es troben a la literatura. Els models de regles ofereixen interpretabilitat i permeten treballar amb els valors dels paràmetres dels algorismes de síntesi, sense processament previ. RuLer, l'algorisme d'aprenentatge proposat, rep dades amb combinacions etiquetades per l'usuari dels valors dels paràmetres d'un algorisme de síntesi. A continuació, analitza els patrons, basats en la dissimilitud, entre les combinacions de cada etiqueta. Aquests patrons es descriuen com un model de regles IF-THEN. Els paràmetres de l'algorisme proporcionen control per definir el que es considera un patró. Llavors, controlen el grau de consistència dels nous paràmetres de síntesi induïts respecte a les dades d'entrada originals. A continuació, es presenta un algorisme (FuzzyRuLer) capaç d’estendre les regles IF-THEN a hiperrectangles, que al seu torn s’utilitzen com a nuclis de funcions de pertinença. El model de regles difuses resultant crea un mapa complet de l'espai de la funció d'entrada. Per això, l'algorisme generalitza les regles lògiques seguint una heurística de volum màxim. Al llarg del manuscrit es discuteix com, quan s’utilitzen algorismes d’aprenentatge automàtic com a eines creatives, de vegades són desitjables glitches, errors o imprecisions produïdes pels models resultants, ja que poden oferir nous resultats imprevisibles. L'avaluació dels algorismes segueix dos camins. El primer es centra en proves d'usuari. El segon, que respon al fet que aquest treball es va dur a terme dins del departament de ciències de la computació, pretén proporcionar una avaluació més àmplia, no específica d'un domini, del rendiment dels algorismes mitjançant benchmarks extrínsecs utilitzats per cross-validation i minority oversampling. En tasques d'oversampling, mitjançant imbalanced data sets, l'algorisme proporciona resultats equiparables als de l'estat de l'art. A més, els punts sintètics produïts són significativament diferents als creats pels altres algorismes i realitzen exploracions (controlades) de regions més llunyanesEste manuscrito explora la programación automática de algoritmos de síntesis de sonido dentro del contexto de la práctica artística performativa conocida como live coding. La escritura de código fuente de forma improvisada para crear música o imágenes, se convirtió en un instrumento en el momento en que las computadoras asequibles pudieron realizar síntesis de sonido en tiempo real con lenguajes que mantuvieron su interprete en funcionamiento. Desde entonces, el live coding ha implicado la programación en tiempo real de algoritmos de síntesis. Para ese propósito, una posibilidad es tener un algoritmo que cree automáticamente variaciones a partir de unos pocos presets seleccionados. Sin embargo, la necesidad de retroalimentación en tiempo real y el pequeño tamaño de los conjuntos de datos (que incluso pueden recopilarse durante la misma actuación), limitan el uso de los algoritmos existentes, tanto de programación automática de sintetizadores como de aprendizaje de máquina. Además, el diseño de dichos algoritmos no está orientado a crear variaciones de un sonido, sino a encontrar los parámetros del sintetizador que coincidan con un sonido dado. Otros enfoques crean representaciones del espacio de posibles sonidos, para permitir al usuario explorarlo mediante evolución interactiva. Aunque estos sistemas están orientados a la exploración, requieren tiempos más largos. Esta tesis investiga el aprendizaje inductivo de reglas para la programación de sintetizadores on-the-fly. Este enfoque es conceptualmente diferente de los que se encuentran en la literatura, tanto de programación de sintetizadores como de live coding. Los modelos de reglas ofrecen interpretabilidad y permiten trabajar con los valores de los parámetros de los algoritmos de síntesis (incluso con datos simbólicos), haciendo innecesario el preprocesamiento. RuLer, el algoritmo de aprendizaje propuesto, recibe un conjunto de datos que contiene combinaciones, etiquetadas por el usuario, de valores de parámetros de un algoritmo de síntesis. Luego, analiza los patrones, en función de la disimilitud, entre las combinaciones de cada etiqueta. Estos patrones se describen como un modelo de reglas lógicas IF-THEN. Los parámetros del algoritmo proporcionan el control para definir qué se considera un patrón. Como los patrones son la base para inducir nuevas configuraciones de parámetros, los parámetros del algoritmo controlan también el grado de consistencia de las configuraciones inducidas con respecto a los datos de entrada originales. Luego, se presenta un algoritmo (llamado FuzzyRuLer) capaz de extender las reglas lógicas tipo IF-THEN a hiperrectángulos, que a su vez se utilizan como núcleos de funciones de pertenencia. El modelo de reglas difusas resultante crea un mapa completo del espacio de las clases de entrada. Para tal fin, el algoritmo generaliza las reglas lógicas resolviendo las contradicciones utilizando una heurística de máximo volumen. A lo largo del manuscrito se analiza cómo, cuando los algoritmos de aprendizaje automático se utilizan como herramientas creativas, los glitches, errores o inexactitudes producidas por los modelos resultantes son a veces deseables, ya que pueden ofrecer resultados novedosos e impredecibles. La evaluación de los algoritmos sigue dos caminos. El primero se centra en pruebas de usuario. El segundo, responde al hecho de que este trabajo se llevó a cabo dentro del departamento de ciencias de la computación y está destinado a proporcionar una evaluación más amplia, no de dominio específica, del rendimiento de los algoritmos utilizando beanchmarks extrínsecos para cross-validation y oversampling. En estas últimas pruebas, utilizando conjuntos de datos no balanceados, el algoritmo produce resultados equiparables a los del estado del arte. Además, los puntos sintéticos producidos son significativamente diferentes de los creados por los otros algoritmos y realizan una exploración (controlada) de regiones más distantes. Finalmente, acompañando la investigación, realicé diversas presentaciones, conciertos y un ´álbum utilizando los algoritmos y ejemplos de esta tesis. Las críticas recibidas y las listas donde se ha presentado el álbum muestran una recepción positiva de la comunidad. En conjunto, estas evaluaciones sugieren que el aprendizaje de reglas es al mismo tiempo un método eficaz y un camino prometedor para futuras investigaciones.Postprint (published version

A Compact Evolutionary Interval-Valued Fuzzy Rule-Based Classification System for the Modeling and Prediction of Real-World Financial Applications With Imbalanced Data

The current financial crisis has stressed the need to obtain more accurate prediction models in order to decrease risk when investing money on economic opportunities. In addition, the transparency of the process followed to make the decisions in financial applications is becoming an important issue. Furthermore, there is a need to handle real-world imbalanced financial datasets without using sampling techniques that might introduce noise in the used data. In this paper, we present a compact evolutionary interval-valued fuzzy rule-based classification system, which is based on interval-valued fuzzy rule-based classification system with tuning and rule selection (IVTURS FA RC-HD ) for the modeling and prediction of real-world financial applications. This proposed system allows obtaining good prediction accuracies using a small set of short fuzzy rules implying a high degree of interpretability of the generated linguistic model. Furthermore, the proposed system deals with the financial imbalanced datasets with no need for any preprocessing or sampling method and, thus, avoiding the accidental introduction of noise in the data used in the learning process. The system is also provided with a mechanism to handle examples that are not covered by any fuzzy rule in the generated rule base. To test the quality of our proposal, we will present an experimental study including 11 real-world financial datasets. We will show that the proposed system outperforms the original C4.5 decision tree, type-1, and interval-valued fuzzy counterparts that use the synthetic minority oversampling technique (SMOTE) to preprocess data and the original FURIA, which is a fuzzy approximative classifier. Furthermore, the proposed method enhances the results achieved by the cost-sensitive C4.5, and it gives competitive results when compared with FURIA using SMOTE, while our proposal avoids preprocessing techniques, and it provides interpretable models that allow obtaining more accurate results